Mixing
How to use Adjacency to transform (¬𝑃∨𝑅)∧(¬𝑃∨𝑄)∧(¬𝑄∨𝑅) into...
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I am going through the accepted proof in this thread. There is a section of the proof that uses Adjacency to transform (¬𝑃∨𝑅)∧(¬𝑃∨𝑄)∧(¬𝑄∨𝑅) into (¬𝑃∨𝑅∨𝑄)∧(¬𝑃∨𝑅∨¬𝑄)∧(¬𝑃∨𝑄)∧(¬𝑄∨𝑅).
It is not obvious to me how this was done.
Can someone show the complete steps of how this is achieved?
Adjacency
$$P = (P lor Q) land (P lor neg Q)$$
logic propositional-calculus boolean-algebra
asked Feb 1 at 14:39
tree_traversaltree_traversal
386
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add a comment |
$begingroup$
I am going through the accepted proof in this thread. There is a section of the proof that uses Adjacency to transform (¬𝑃∨𝑅)∧(¬𝑃∨𝑄)∧(¬𝑄∨𝑅) into (¬𝑃∨𝑅∨𝑄)∧(¬𝑃∨𝑅∨¬𝑄)∧(¬𝑃∨𝑄)∧(¬𝑄∨𝑅).
It is not obvious to me how this was done.
Can someone show the complete steps of how this is achieved?
Adjacency
$$P = (P lor Q) land (P lor neg Q)$$
logic propositional-calculus boolean-algebra
asked Feb 1 at 14:39
tree_traversaltree_traversal
386
$endgroup$
add a comment |
$begingroup$
I am going through the accepted proof in this thread. There is a section of the proof that uses Adjacency to transform (¬𝑃∨𝑅)∧(¬𝑃∨𝑄)∧(¬𝑄∨𝑅) into (¬𝑃∨𝑅∨𝑄)∧(¬𝑃∨𝑅∨¬𝑄)∧(¬𝑃∨𝑄)∧(¬𝑄∨𝑅).
It is not obvious to me how this was done.
Can someone show the complete steps of how this is achieved?
Adjacency
$$P = (P lor Q) land (P lor neg Q)$$
logic propositional-calculus boolean-algebra
asked Feb 1 at 14:39
tree_traversaltree_traversal
386
$endgroup$
I am going through the accepted proof in this thread. There is a section of the proof that uses Adjacency to transform (¬𝑃∨𝑅)∧(¬𝑃∨𝑄)∧(¬𝑄∨𝑅) into (¬𝑃∨𝑅∨𝑄)∧(¬𝑃∨𝑅∨¬𝑄)∧(¬𝑃∨𝑄)∧(¬𝑄∨𝑅).
It is not obvious to me how this was done.
Can someone show the complete steps of how this is achieved?
Adjacency
$$P = (P lor Q) land (P lor neg Q)$$
logic propositional-calculus boolean-algebra
logic propositional-calculus boolean-algebra
asked Feb 1 at 14:39
tree_traversaltree_traversal
386
asked Feb 1 at 14:39
tree_traversaltree_traversal
386
asked Feb 1 at 14:39
tree_traversaltree_traversal
386
asked Feb 1 at 14:39
tree_traversaltree_traversal
386
asked Feb 1 at 14:39
tree_traversaltree_traversal
386
386
add a comment |
add a comment |
1 Answer
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The $neg P lor R$ gets transformed into $(neg P lor R lor Q) land (neg P lor R lor neg Q)$:
$$neg P lor R overset{Adjacency}{=}$$
$$((neg P lor R) lor Q) land ((neg P lor R) lor neg Q) overset{Association}{=}$$
$$((neg P lor R) lor Q) land ((neg P lor R) lor neg Q)$$
So in terms of Pattern Matching:
The '$P$' is $neg P lor R$, while the '$Q$' is $Q$
answered Feb 1 at 14:41
Bram28Bram28
64.4k44793
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$begingroup$
This answers my question. Writing to let you know I will accept your answer but I have to wait 8 minutes to do so. Would upvote but can't do that either. Thanks for the help!
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– tree_traversal
Feb 1 at 14:46
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@tree_traversal Don't worry about it. In fact, I shouldn't be gaining rep on a clarification on my own Answer! :)
$endgroup$
– Bram28
Feb 1 at 14:51
add a comment |
Your Answer
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1 Answer
1
active
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The $neg P lor R$ gets transformed into $(neg P lor R lor Q) land (neg P lor R lor neg Q)$:
$$neg P lor R overset{Adjacency}{=}$$
$$((neg P lor R) lor Q) land ((neg P lor R) lor neg Q) overset{Association}{=}$$
$$((neg P lor R) lor Q) land ((neg P lor R) lor neg Q)$$
So in terms of Pattern Matching:
The '$P$' is $neg P lor R$, while the '$Q$' is $Q$
answered Feb 1 at 14:41
Bram28Bram28
64.4k44793
$endgroup$
$begingroup$
This answers my question. Writing to let you know I will accept your answer but I have to wait 8 minutes to do so. Would upvote but can't do that either. Thanks for the help!
$endgroup$
– tree_traversal
Feb 1 at 14:46
$begingroup$
@tree_traversal Don't worry about it. In fact, I shouldn't be gaining rep on a clarification on my own Answer! :)
$endgroup$
– Bram28
Feb 1 at 14:51
add a comment |
$begingroup$
The $neg P lor R$ gets transformed into $(neg P lor R lor Q) land (neg P lor R lor neg Q)$:
$$neg P lor R overset{Adjacency}{=}$$
$$((neg P lor R) lor Q) land ((neg P lor R) lor neg Q) overset{Association}{=}$$
$$((neg P lor R) lor Q) land ((neg P lor R) lor neg Q)$$
So in terms of Pattern Matching:
The '$P$' is $neg P lor R$, while the '$Q$' is $Q$
answered Feb 1 at 14:41
Bram28Bram28
64.4k44793
$endgroup$
$begingroup$
This answers my question. Writing to let you know I will accept your answer but I have to wait 8 minutes to do so. Would upvote but can't do that either. Thanks for the help!
$endgroup$
– tree_traversal
Feb 1 at 14:46
$begingroup$
@tree_traversal Don't worry about it. In fact, I shouldn't be gaining rep on a clarification on my own Answer! :)
$endgroup$
– Bram28
Feb 1 at 14:51
add a comment |
$begingroup$
The $neg P lor R$ gets transformed into $(neg P lor R lor Q) land (neg P lor R lor neg Q)$:
$$neg P lor R overset{Adjacency}{=}$$
$$((neg P lor R) lor Q) land ((neg P lor R) lor neg Q) overset{Association}{=}$$
$$((neg P lor R) lor Q) land ((neg P lor R) lor neg Q)$$
So in terms of Pattern Matching:
The '$P$' is $neg P lor R$, while the '$Q$' is $Q$
answered Feb 1 at 14:41
Bram28Bram28
64.4k44793
$endgroup$
The $neg P lor R$ gets transformed into $(neg P lor R lor Q) land (neg P lor R lor neg Q)$:
$$neg P lor R overset{Adjacency}{=}$$
$$((neg P lor R) lor Q) land ((neg P lor R) lor neg Q) overset{Association}{=}$$
$$((neg P lor R) lor Q) land ((neg P lor R) lor neg Q)$$
So in terms of Pattern Matching:
The '$P$' is $neg P lor R$, while the '$Q$' is $Q$
answered Feb 1 at 14:41
Bram28Bram28
64.4k44793
edited Feb 1 at 14:42
answered Feb 1 at 14:41
Bram28Bram28
64.4k44793
answered Feb 1 at 14:41
Bram28Bram28
64.4k44793
answered Feb 1 at 14:41
Bram28Bram28
64.4k44793
64.4k44793
$begingroup$
This answers my question. Writing to let you know I will accept your answer but I have to wait 8 minutes to do so. Would upvote but can't do that either. Thanks for the help!
$endgroup$
– tree_traversal
Feb 1 at 14:46
$begingroup$
@tree_traversal Don't worry about it. In fact, I shouldn't be gaining rep on a clarification on my own Answer! :)
$endgroup$
– Bram28
Feb 1 at 14:51
add a comment |
$begingroup$
This answers my question. Writing to let you know I will accept your answer but I have to wait 8 minutes to do so. Would upvote but can't do that either. Thanks for the help!
$endgroup$
– tree_traversal
Feb 1 at 14:46
$begingroup$
@tree_traversal Don't worry about it. In fact, I shouldn't be gaining rep on a clarification on my own Answer! :)
$endgroup$
– Bram28
Feb 1 at 14:51
$begingroup$
This answers my question. Writing to let you know I will accept your answer but I have to wait 8 minutes to do so. Would upvote but can't do that either. Thanks for the help!
$endgroup$
– tree_traversal
Feb 1 at 14:46
$begingroup$
This answers my question. Writing to let you know I will accept your answer but I have to wait 8 minutes to do so. Would upvote but can't do that either. Thanks for the help!
$endgroup$
– tree_traversal
Feb 1 at 14:46
$begingroup$
@tree_traversal Don't worry about it. In fact, I shouldn't be gaining rep on a clarification on my own Answer! :)
$endgroup$
– Bram28
Feb 1 at 14:51
$begingroup$
@tree_traversal Don't worry about it. In fact, I shouldn't be gaining rep on a clarification on my own Answer! :)
$endgroup$
– Bram28
Feb 1 at 14:51
add a comment |
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